Question

In Fig, AB ∥ CD and a transversal PQ cuts at L and M respectively. If ∠QMD = 100°, find all the other angles.

Answer 1

Given that, AB ∥ CD and ∠QMD = 100°

We know that, from the figure ∠QMD + ∠QMC = 180° is a linear pair,

∠QMC = 180° – ∠QMD

∠QMC = 180° – 100°

∠QMC = 80°

Corresponding angles are

∠DMQ = ∠BLM = 100°

∠CMQ = ∠ALM = 80°

Vertically Opposite angles are

∠DMQ = ∠CML = 100°

∠BLM = ∠PLA = 100°

∠CMQ = ∠DML = 80°

∠ALM = ∠PLB = 80°